In order to reduce the computational cost, variational inference is applied in VHGPR, which uses parameterized Gaussian distributions to approximate some critical distributions involved in the posterior and likelihood function. These Gaussian distributions can be determined efficiently through some optimization problem to minimize their differences from the critical distributions.
As a result of this approximation, the high-dimensional integration can be reduced to analytical formulations which leads to inexpensive computations (approximations) of the posterior and the likelihood function. More details on the algorithms of the VHGPR, along with SGPR, are summarized in Appendix A for completeness. The interested readers can also refer to [1]}, [2]} for details.
